A Lower Bound for the Fisher Information Measure

Stein, Manuel; Mezghani, Amine; Nossek, Josef A.

doi:10.1109/lsp.2014.2316008

Cited by 51 publications

(66 citation statements)

References 9 publications

(14 reference statements)

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“…For the TEM measurement, on the other hand, and using the lower bound by Stein et al [71], I obtain¯(…”

Section: Quantum Limitsmentioning

confidence: 99%

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

Tsang¹

2017

New J. Phys.

130

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I propose a spatial-mode demultiplexing (SPADE) measurement scheme for the far-field imaging of spatially incoherent optical sources. For any object too small to be resolved by direct imaging under the diffraction limit, I show that SPADE can estimate its second or higher moments much more precisely than direct imaging can fundamentally do in the presence of photon shot noise. I also prove that SPADE can approach the optimal precision allowed by quantum mechanics in estimating the location and scale parameters of a subdiffraction object. Realizable with far-field linear optics and photon counting, SPADE is expected to find applications in both fluorescence microscopy and astronomy.

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“…For the TEM measurement, on the other hand, and using the lower bound by Stein et al [71], I obtain¯(…”

Section: Quantum Limitsmentioning

confidence: 99%

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

Tsang¹

2017

New J. Phys.

130

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“…A more general result was recently proven by Stein et al [51], which says that given a multidimensional random variable with density function f X;θ with:…”

Section: Lower Bound For Fisher Informationmentioning

confidence: 97%

Fisher Information Properties

Zegers

2015

Entropy

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A set of Fisher information properties are presented in order to draw a parallel with similar properties of Shannon differential entropy. Already known properties are presented together with new ones, which include: (i) a generalization of mutual information for Fisher information; (ii) a new proof that Fisher information increases under conditioning; (iii) showing that Fisher information decreases in Markov chains; and (iv) bound estimation error using Fisher information. This last result is especially important, because it completes Fano's inequality, i.e., a lower bound for estimation error, showing that Fisher information can be used to define an upper bound for this error. In this way, it is shown that Shannon's differential entropy, which quantifies the behavior of the random variable, and the Fisher information, which quantifies the internal structure of the density function that defines the random variable, can be used to characterize the estimation error.

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“…Alternatively, Stein et al [101] prove that the Fisher information for the mean of any distribution is bounded below by the inverse of its variance…”

Section: Fisher Information Matrix For Ir Imagementioning

confidence: 99%

Optimal 6D Object Pose Estimation with Commodity Depth Sensors

Landau

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Accurate 6D object pose estimation, as well as other model-based shape matching objectives such as object detection, classification, and shape inspection, is prominent and necessary in a large number of domains and applications. This includes household and robotics applications to automate various tasks, where input depth measurements are aligned to a corresponding model of the object, such as a CAD that is composed of several interconnected parts, depending on the model's level of detail and complexity. Industrial metrology systems also compare the shapes of engineered components and equipment to their corresponding 3D models for quality assessment and anomaly detection; this often requires very costly and high resolution projection and detection mechanisms. Structuredlight laser scanners have, however, emerged as a viable option to provide cheap and reasonably accurate depth estimates, which have recently become commodity-priced within this decade due to the maturity of the technology. These sensors are also robust for semi-transparent and reflective surfaces, dynamic scenery, ambient background light, and temperature drift. Certain structured-light light coding methods unfortunately need to implement a complicated, non-invertible transformation of a distorted light pattern to generate the pixel-by-pixel depth estimates, thereby leading to a loss of information. This can result in poorly estimated or even missing depth data, especially when the object has small 3D features or non-ideal surface properties. Moreover, the informative rigid body constraint is blurred when the nonlinear 2D depth image to 3D pseudo-measurement point cloud transformation is applied, which is the domain where most model-based shape matching methods operate.Alternatively, estimating pose from information early in the structured-light sensing/processing chain has the potential to alleviate errors induced in subsequent nonlinear processing steps that are in fact locally scene dependent. This motivates one of the main contributions from this dissertation, which presents an asymptotically optimal maximum likelihood estimation method that operates directly on the raw output IR images. This is made possible by an extensive study on a commonly utilized commodity-priced structured-light sensor, which contributed to the proposed high-fidelity IR and depth image predictor and simulator that models the physics of the transmit and receive optics,

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A Lower Bound for the Fisher Information Measure

Cited by 51 publications

References 9 publications

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing

Fisher Information Properties

Optimal 6D Object Pose Estimation with Commodity Depth Sensors

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